# Alternating Estimation Series Theorem

• April 10th 2010, 11:23 PM
alleysan
Alternating Estimation Series Theorem
Hello,

I am having problems understanding Alternating Series Estimation Theorem...

http://i39.tinypic.com/k9uwc9.png

For the 2nd half of the question (finding the natural number of n)... (ignore the equal signs, I was getting desperate), I thought that like the other tests like convergence, limit comparison, etc that
$b_{n+1} < error$
with the error being the 0.004?
But that is apparently wrong. I double checked my algebra and it is correct... so it is just a signage error.

If anybody could even give a hint, that would be greatly appreciated... this whole chapter on series and sequences is confusing.

Thanks a bunch?
• April 11th 2010, 04:26 AM
HallsofIvy
Everything is correct but for the last step.

You want $b_n= \frac{1}{3(3^n)+ 7}\le .004$ (not "=") and that gives, just as you say, $3^n\ge \frac{1- .004(7)}{3(.004)}= 81$.

Then n= 4, not 3.